Initial Commit

Common/Auxiliary/TriangleMath.cs

@@ -0,0 +1,73 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Windows;
+using System.Windows.Media.Media3D;
+
+namespace Microsoft.Research.DynamicDataDisplay.Common.Auxiliary
+{
+	public static class TriangleMath
+	{
+		public static bool TriangleContains(Point a, Point b, Point c, Point m)
+		{
+			double a0 = a.X - c.X;
+			double a1 = b.X - c.X;
+			double a2 = a.Y - c.Y;
+			double a3 = b.Y - c.Y;
+
+			if (AreClose(a0 * a3, a1 * a2))
+			{
+				// determinant is too close to zero => apexes are on one line
+				Vector ab = a - b;
+				Vector ac = a - c;
+				Vector bc = b - c;
+				Vector ax = a - m;
+				Vector bx = b - m;
+				bool res = AreClose(ab.X * ax.Y, ab.Y * ax.X) && !AreClose(ab.LengthSquared, 0) ||
+					AreClose(ac.X * ax.Y, ac.Y * ax.X) && !AreClose(ac.LengthSquared, 0) ||
+					AreClose(bc.X * bx.Y, bc.Y * bx.X) && !AreClose(bc.LengthSquared, 0);
+				return res;
+			}
+			else
+			{
+				double b1 = m.X - c.X;
+				double b2 = m.Y - c.Y;
+
+				// alpha, beta and gamma - are baricentric coordinates of v 
+				// in triangle with apexes a, b and c
+				double beta = (b2 / a2 * a0 - b1) / (a3 / a2 * a0 - a1);
+				double alpha = (b1 - a1 * beta) / a0;
+				double gamma = 1 - beta - alpha;
+				return alpha >= 0 && beta >= 0 && gamma >= 0;
+			}
+		}
+
+		private const double eps = 0.00001;
+		private static bool AreClose(double x, double y)
+		{
+			return Math.Abs(x - y) < eps;
+		}
+
+		public static Vector3D GetBaricentricCoordinates(Point a, Point b, Point c, Point m)
+		{
+			double Sac = GetSquare(a, c, m);
+			double Sbc = GetSquare(b, c, m);
+			double Sab = GetSquare(a, b, m);
+
+			double sum = (Sab + Sac + Sbc) / 3;
+
+			return new Vector3D(Sbc / sum, Sac / sum, Sab / sum);
+		}
+
+		public static double GetSquare(Point a, Point b, Point c)
+		{
+			double ab = (a - b).Length;
+			double ac = (a - c).Length;
+			double bc = (b - c).Length;
+
+			double p = 0.5 * (ab + ac + bc); // half of perimeter
+			return Math.Sqrt(p * (p - ab) * (p - ac) * (p - bc));
+		}
+	}
+}